A guitar string is supposed to be played with a fundamental frequency of 880 Hz. If it is determined to have, instead, a fundamental frequency of 882 Hz, by what amount (as a percentage) must the tension in the string be changed in order that the fundamental frequency be restored to 880 Hz?
A) −0.45%
B) +0.45%
C) −0.11%
D) −0.23%

Question

Quizplus · Accepted Answer

The frequency of a vibrating string is proportional to the square root of the tension. To decrease the frequency from 882 Hz to 880 Hz, the tension must be decreased. The percentage change in tension is calculated using the formula: (f2/f1)^2 - 1, where f2 is the desired frequency and f1 is the current frequency. Substituting the values, ((880/882)^2 - 1) gives approximately -0.45%.

A Guitar String Is Supposed to Be Played with a Fundamental